Data-Driven Robust Optimization using Unsupervised Deep Learning

TL;DR

This paper introduces an unsupervised deep learning approach to derive data-driven uncertainty sets for robust optimization, resulting in more accurate and robust decision solutions compared to traditional methods.

Contribution

It presents a novel method using unsupervised deep learning to extract complex uncertainty sets from data, improving robustness and solution quality in optimization problems.

Findings

Unsupervised deep learning-derived sets better capture data structure.

The approach outperforms kernel-based support vector clustering in experiments.

Robust solutions achieved are both more feasible and have better objective values.

Abstract

Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called the uncertainty set. An ongoing challenge in the recent literature is to derive uncertainty sets from given historical data that result in solutions that are robust regarding future scenarios. In this paper we use an unsupervised deep learning method to learn and extract hidden structures from data, leading to non-convex uncertainty sets and better robust solutions. We prove that most of the classical uncertainty classes are special cases of our derived sets and that optimizing over them is strongly NP-hard. Nevertheless, we show that the trained neural networks can be integrated into a robust optimization model by formulating the adversarial problem as a convex quadratic mixed-integer program. This allows us to derive robust solutions through an iterative scenario generation process. In our computational experiments, we compare this approach to a similar approach using kernel-based support vector clustering. We find that uncertainty sets derived by the unsupervised deep learning method find a better description of data and lead to robust solutions that outperform the comparison method both with respect to objective value and feasibility.